Education
Class 10 Mathematics Unit 1 & Unit 2 Model Paper 2027 | Complex Numbers, Quadratic Equations and Inequalities | Board Standard
Class 10 Math Model Paper 2027
Class 10 Mathematics Model Paper 2027 covering Unit 1: Complex Numbers and Unit 2: Quadratic Equations and Inequalities is designed according to a board-standard paper pattern. This Class 10 Mathematics Model Paper 2027 includes objective and subjective-type questions, short questions, and detailed questions based on important concepts from Complex Numbers and Quadratic Equations and Inequalities. It is useful for Class 10 Mathematics exam preparation, revision, practice tests, and students preparing for the 2027 Board Examination.
786Times
786Times
786Times
786Times
786Times
PAPER NO.
01
MATHEMATICS
CHAPTER
WISE
Roll No. (in Figures):
(in Words):
Unit 1: Complex Numbers
Unit 2: Quadratic Equations and Inequalities
Unit 2: Quadratic Equations and Inequalities
OBJECTIVE TYPE
Time : 20 Minutes
Marks : 15
Marks : 15
1ABCD
2ABCD
3ABCD
4ABCD
5ABCD
6ABCD
7ABCD
8ABCD
9ABCD
10ABCD
11ABCD
12ABCD
13ABCD
14ABCD
15ABCD
Note: Four possible answers A, B, C and D to each question are given.
The choice which you think is correct, fill that circle in front of that question with
Marker or Pen ink. Cutting or filling two or more circles will result in zero mark in that question.
Q1. 15
1. Real part of (2 − 3i)(2 + 3i) is:
2. What is additive inverse of 5 − 2i?
3. If z = 4 − 3i, then z z̄ =
4. Conjugate of 9 − 4i is:
5. The imaginary unit is represented by:
6. The idea of complex numbers first emerged in:
7. (4 − 3i) − (2 − 5i) = ______
8. The number (2 − 7i) is equivalent to:
9. The solution set of 3x² − 9 = 0 is:
10. Product of the roots of 3x² + 5x − 12 = 0 is:
11. 3 and 2 are the roots of:
12. If b² − 4ac > 0 and is a perfect square, then the roots of ax² + bx + c = 0 are:
13. An equation of the form ax² + bx + c = 0 becomes pure quadratic equation when:
14. The point of intersection of y = 2x + 4 with x-axis graphically is:
15. The expression b² − 4ac in a quadratic equation is known as:
Here is subjective Part of Class 10 th Model Paper from Unit No.No.1 and it No. 2
786Times
786Times
786Times
786Times
786Times
Roll No. (in Figures):
(in Words):
Unit 1: Complex Numbers
Unit 2: Quadratic Equations and Inequalities
Unit 2: Quadratic Equations and Inequalities
Time : 2:10 Hours
Marks: 60
Marks: 60
SUBJECTIVE TYPE (PART – I)
Q2. Write short answers to any SIX (6) questions:
(6×2=12)
(i) Is “0” a complex number? Explain.
(ii) State the condition for two complex numbers to be equal.
(iii) Simplify: (3 − 4i)(5 − 6i)
(iv) If z₁ = 5 + 4i, and z₂ = 3 + 2i, then find z₁z₂.
(v) Find real and imaginary parts of z = (2 + 7i)⁻¹.
(vi) Why does the equation x² + 1 = 0 has no “real” solution?
(vii) Find additive and multiplicative inverse of z = 8 + 9i.
(viii) Simplify: (17 − 7i) + (19 − 7i)
(ix) If z₁ + z₂ = 19 − 11i and z₁ = 3 − 7i then find z₂.
Q3. Write short answers to any SIX (6) questions:
(6×2=12)
(i) Express (2 + √3i)(−7 + 2i) in the form of a + bi.
(ii) If z₁ = 2 + 3i and z₂ = 4 + i, show that the commutative property of addition holds.
(iii) Write the Associative property for multiplication of complex numbers.
(iv) What is an Argand Plane?
(v) Examine the nature of the roots of the equation:
15x² + 11x + 2 = 0.
(vi) Examine the nature of the roots of the equation:
x² − x − 1 = 0.
(vii) If a ball is thrown upward with a velocity v, the maximum height it reaches can be determined by using a formula
h = v²/2g. Rearrange the formula to make v the subject.
(viii) What is the standard form of a quadratic equation?
(ix) Solve the equation x² + 2x − 35 = 0 by factorization method.
Q4. Write short answers to any SIX (6) questions:
(6×2=12)
(i) Solve the equation by completing square method:
x² − 2x − 889 = 0.
(ii) Write the formula for the sum of the roots of a quadratic equation.
(iii) What happens to the product of the roots if constant term c is zero?
(iv) What is the discriminant of the equation ax² + bx + c = 0?
(v) Describe the nature of roots if b² − 4ac > 0 and is a perfect square.
(vi) Examine the nature of the roots 25x² − 30x + 9 = 0.
(vii) Examine the nature of the roots of x² − 7x + 12 = 0.
(viii) If y² = 4ax, make ‘a’ as the subject of the equation.
(ix) If I = PRT then make ‘R’ the subject of this formula.
(PART – II)
Note: Attempt any two (02) questions.
(2×8=16)
Q5. (a)
If
(1 + i)² / (2 − i) = x + iy
then find the values of x and y.
4
(b)
If (2x + iy)(1 − i) = 4 + 2i, then find the values of x and y.
4
Q6. (a)
If z = 4 − 3i, then verify that
|z| = |−z| = |z̄| = |−z̄|.
4
(b)
Find real and imaginary parts of (4 + 3i)⁻¹.
4
Q7. (a)
Find real and imaginary parts of z = (4 + 3i)⁻².
4
(b)
Find the sum and the product of the roots of the equation
3x² + 5x − 12 = 0 without solving.
4
(PART – III)
Note: Attempt any one (01) question.
(1×8=8)
Q8. (a)
Find the condition that the roots of
ax² + bx + c = 0 may be equal in magnitude but opposite in sign,
where a ≠ 0.
4
(b)
If the quadratic equation 16x² + 7px + 49 = 0 has equal roots,
then find the values of p.
4
Q9. (a)
Solve x² − 5x + 2 = 0 by using the quadratic formula.
4
(b)
Find the point of intersecting of the linear equation
y = 2 + 3x with coordinate axes graphically.
4
